Answer
$\text{(a)}$ $23$.
$\text{(b)}$ $7$.
$\text{(c)}$ $47$
Work Step by Step
Given $f(x)=8x^2-x$, the average rate of change $R$ is given by the formula
$$R=\frac{f(x_2)-f(x_1)}{x_2-x_1}$$
Thus,
$\text{(a)}$ For $x_1=1, x_2=2$, we have:
$R=\dfrac{f(2)-f(1)}{2-1}=\dfrac{8(2)^2-(2)-[8(1)^2-(1)]}{1}=23$.
$\text{(b)}$ For $x_1=0, x_2=1$, we have:
$R=\dfrac{f(1)-f(0)}{1-0}=\dfrac{8(1)^2-(1)-[8(0)^2-(0)]}{1}=7$.
$\text{(c)}$ For $x_1=2, x_2=4$, we have:
$R=\dfrac{f(4)-f(2)}{4-2}=\dfrac{8(4)^2-(4)-[8(2)^2-(2)]}{2}=47$.
